The French chemists Pierre L. Dulong and Alexis T. Petit noted in 1819 that the

Question

The French chemists Pierre L. Dulong and Alexis T. Petit noted in 1819 that the molar heat capacity of many solids at ordinary temperatures is proportional to the number of atoms per formula unit of the solid. They quantified their observations in what is known as Dulong and Petit's rule, which says that the molar heat capacity, Cp, of a solid can be expressed as C_P=N 3R where N is the number of atoms per formula unit and R is the universal gas constant. The observed heat capacity per gram of a compound containing thallium and chlorine is 0.21 J K^-1. g^-1. Use Dulong and Petit's rule to determine the empirical formula of the compound. Calculate the heat energy released when 18.2 g of liquid mercury at 25.00 degree C is converted to solid mercury at its melting point. Constants for mercury at 1 atm

Explanation / Answer

R = 8.3145 J/K·mol
3R = 24.94 J/K·mol

Now we Try several possibilities as follows:

TlCl
N = 2
molar mass = 239.8365 g/mol
2 x (24.94 J/K·mol) / (239.8365 g/mol) = 0.2079 J/K·g

TlCl2
N = 3
molar mass = 275.2897 g/mol
3 x (24.94 J/K·mol) / (275.2897 g/mol) = 0.2718 J/K·g

Tl2Cl
N = 3
molar mass = 444.2198 g/mol
3 x (24.94 J/K·mol) / (444.2198 g/mol) = 0.1684 J/K·g

Here the given compound is TlCl because its heat capacity is very near.

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